A new proof of James' sup theorem
arXiv:math/0505176
Abstract
We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson (1977) : "If a normed space does not contain any asymptotically isometric copy of $\ell^1(\IN)$, then every bounded sequence of has a normalized block sequence pointwise converging to 0".